Stochastic representations of ion channel kinetics and exact stochastic simulation of neuronal dynamics
Stochastic representations of ion channel kinetics and exact stochastic simulation of neuronal dynamics
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DOI：
10.1007/s10827-014-0528-2
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发表时间：
2015-02-01
影响因子：
1.2
通讯作者：
Thomas, Peter J.
中科院分区：
文献类型：
--
作者：
Anderson, David F.;Ermentrout, Bard;Thomas, Peter J.
本文给出了随机离子通道动力学的两种表示，并将精确模拟的性能与常用的数值逼近策略进行了比较。我们给出的第一个表示是随机时变表示，由Thomas Kurtz推广，第二个类似于“Gillesbie”表示。对于不同的表示，提供了精确的随机算法，这比文献中仍然出现的(A)固定时间步长或(B)分段恒定倾向算法更可取。作为例子，我们提供了基于Morris-LeCar电导模型的精确算法的版本，并详细说明了在该模型上使用近似算法所引起的弱和强意义上的误差。我们在XPP和MatLab中都包含了随机时变算法的现成实现。最后，通过对参数敏感度分析的考虑，我们展示了所给出的表示在进一步的计算方法的发展中是如何有用的。这里提供的一般表述和模拟策略在科学的其他部分是已知的，但在目前的背景下不太清楚。
In this paper we provide two representations for stochastic ion channel kinetics, and compare the performance of exact simulation with a commonly used numerical approximation strategy. The first representation we present is a random time change representation, popularized by Thomas Kurtz, with the second being analogous to a "Gillespie" representation. Exact stochastic algorithms are provided for the different representations, which are preferable to either (a) fixed time step or (b) piecewise constant propensity algorithms, which still appear in the literature. As examples, we provide versions of the exact algorithms for the Morris-Lecar conductance based model, and detail the error induced, both in a weak and a strong sense, by the use of approximate algorithms on this model. We include ready-to-use implementations of the random time change algorithm in both XPP and Matlab. Finally, through the consideration of parametric sensitivity analysis, we show how the representations presented here are useful in the development of further computational methods. The general representations and simulation strategies provided here are known in other parts of the sciences, but less so in the present setting.